[tex]\it \Delta MDC\sim \Delta MAB \Rightarrow k=\dfrac{DC}{AB}=\dfrac{12^{(6}}{30}=\dfrac{2}{5}\\ \\ \\ \dfrac{\mathcal{A}_{MDC}}{\mathcal{A _{MAB}}} = k^2 = \Big( \dfrac{2}{5}\Big)^2 \Rightarrow \dfrac{\mathcal{A}_{MDC}}{\mathcal{A _{MAB}}} = \dfrac{4}{25} \stackrel{derivare}{\Longrightarrow}\ \dfrac{\mathcal{A}_{MDC}}{\mathcal{A} _{MAB}-\mathcal{A}_{MDC}} = \dfrac{4}{25-4} \Rightarrow\\ \\ \\ \Rightarrow \dfrac{\mathcal{A}_ {MDC}}{\mathcal{A}_{ABCD}}=\dfrac{4}{21}\ \ \ \ \ (1)[/tex]
[tex]\it p\%\ din\ \mathcal{A}_{ABCD}=\mathcal{A}_{MDC} \Rightarrow \dfrac{p}{100}\cdot\mathcal{A}_{ABCD}=\mathcal{A}_{MDC} \Rightarrow p\cdot\dfrac{\mathcal{A}_{ABCD}}{100}=\mathcal{A}_{MDC}\Rightarrow \\ \\ \\ \Rightarrow p=\mathcal{A}_{MDC}\cdot\dfrac{100}{\mathcal{A}_{ABCD}}=\dfrac{\mathcal{A}_{MDC}}{\mathcal{A}_{ABCD}}\cdot100\ \ \ \ \ (2)\\ \\ \\ (1),\ (2)\Rightarrow p=\dfrac{4}{21}\cdot100=\dfrac{400}{21}\approx19,04[/tex]
Prin urmare, procentul cerut este 19,04%.
